Huge increase of memory use when increasing the resolution
If you see memory usage changing while rendering, it could be because of Denoising enabled, try:


lowering the render tile size
changing the tile order (from Hilbert to Left-to-right), so the minimum number of tiles are kept in memory
disabling Denoising altogether


Explanation why extra memory has to be used for denoising is here:

Why does Denoising take up so much memory?